Though Rydberg atoms have kindled the flame for the ambition to large-scale quantum computing [1]}, [2]}, [3]}, [4]}, [5]}, and recent experiments demonstrated remarkable advances [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, [14]}, [15]}, [16]}, [17]}, [18]}, further progress toward neutral-atom quantum computing is hindered by the difficulty to prepare a fast and accurate CNOT. This is partly because each of those CNOT gates was realized via combining an EA-based controlled-Z (\(C_Z\) ) and a series of single-qubit gates [7]}, [8]}, [9]}, [11]}, [15]}, [14]}, leading to CNOT durations dominated by single-qubit operations (e.g., over \(4~\mu \) s in [14]}, [15]}). In contrast, an TSD-based CNOT has a duration about \(2\pi /\Omega +\epsilon \)  by only two Rydberg pulses, i,e., needs no single-qubit rotations, where \(\epsilon \)  is a transient moment to implement a phase change in the pulses and \(\Omega \)  the Rydberg Rabi frequency. Using values of \(\Omega \)  and \(\epsilon \)  from [15]}, [14]}, the TSD-based CNOT (duration \(\sim 0.3~\mu \) s) would be orders of magnitude faster than those in [15]}, [14]}, which means that a neutral-atom CNOT can be much faster than the CNOT (or ground Bell-state gate) by trapped ions [31]}, [32]}, [33]}, [34]}, [35]} (notice that the fast ion-trap gates in [36]}, [37]} are phase gates). Although still inferior to superconducting circuits [38]}, [39]} where CNOT gate times can be around 50 ns [40]}, the TSD-based CNOT is applicable in scalable neutral-atom platforms that are ideal for long-lived storage of quantum information in room temperatures.
